How do I form planes into existing object?
You could do it with a procedural texture, but if you absolutely want to use an image texture, I see at least two ways to do it, tell me if it answers.


First, as Keavon says, you could UVmap your object with a texture.
Prepare your texture, it needs to be tileable.
As your object is already made, create a seam along an edge, and unwrap.





Your object is not orthogonal, so it will be displayed as a twisted mesh in the UV/Image Editor. It won't allow the image texture to be repeated seamlessly, so you need to orthogonalize your UV. To do that you need to use an addon like UV Squares. Once installed, open the T panel on the left of the UV/Image Editor window > Misc, press To Square Grid. Rescale the UV on the Y axis and on all axis, move it...





Don't forget to plug the Image Texture node into a Diffuse in the Shader Editor. Now your uvmap is orthogonal and the image texture will repeat seamlessly. Advantage of this method: you need only one picture and it doesn't need to be big as it is repeated. Small problem with this method: the texture may be a bit distorted on some parts.





The second method would be to paint the texture on your whole object.
Prepare a second material, create a second UV map for this one, this time unwrap with the Smart UV Project mode. Create a new (black) image in the UV/Image Editor with the "+" button. This image needs to be large enough because it will have to cover the whole object, so you need to decide, depending on your final goal. Plug the Image Texture node in the Diffuse, and load this new image. Put an Input > UV Map node before if you've created a second UV map.





In the 3D View switch to Texture Paint mode. In the T panel > Tools > Texture, create a new texture, and in the Properties panel > Texture, choose Brush - Texture to determine what texture you will use for your brush, choose your cave wall texture (doesn't need to be tileable this time).





On the T panel > Tools > Texture > Brush Mapping, choose Stencil. It will overlay the texture image on the 3D View and allow you to project it on your object. To be complete about stencil, how to change its position here.





You should be able to paint your object, and the painting will appear on the new image you've created in the UV/Image Editor. Advantage of this method: You can apply the texture as you want on the object, it may look more natural. Disavantage: As it is not a repeated pattern you need a big image that covers all your object.


 

With both the 2 methods, to make everything more realistic you need to complicate a bit your nodes organisation: add glossiness and bump maps, etc...